Approaches for unsupervised identification of data-driven models for flow forecasting in urban drainage systems

In this work, an unsupervised model selection procedure for identifying data-driven forecast models for urban drainage systems is proposed and evaluated. Specifically, we consider the case of predicting inflows to wastewater treatment plants for activating wet weather operation (aeration tank settling, ATS) using Box–Jenkins models.

The model selection procedure considers different model structures and different objective functions. The hyperparameter search space is constrained based on the time of concentration in the catchment. Objective function criteria that minimize one-step-ahead as well as multi-step prediction errors are considered.

Finally, we consider two criteria for unsupervised selection of the best-performing model. These measure the agreement of observed and predicted hydrographs (persistence index), as well as the binary exceedance of critical flow thresholds (critical success index (CSI)). Our work shows that forecast models can be developed in an unsupervised manner, and ATS activation is correctly forecasted in 60–90% of the events.

The selected model structures reflect the physical behaviour of the catchment. Models should not be selected on operational criteria like the CSI due to a risk of overfitting. The degree to which rainfall input improves forecasts depends on the specific catchment, and the objective function criterion that should be used for coefficient estimation depends on the application context.